Currently Being ModeratedSep 2, 2013 11:30 PM (in response to Puelum)
The most likely cause is a worn out battery that is no longer able to hold a charge. When it is connected, it gets power from the USB port so it works are expected and appears to charge. When you disconnect it, the battery does not hold the charge for more than a few seconds, and the shuffle is therefore dead.
Currently Being ModeratedSep 4, 2013 11:22 AM (in response to Puelum)
It's not good to store a rechargeable lithium-based battery completely discharged for an extended period. The chemicals that make the battery work will age in a way can make the battery incapable of holding a charge. Since that's a 2nd gen shuffle, it's been sitting unused for about six years. I have a 2nd gen shuffle, and it still works well, but I've charging and discharging the battery at least once each month through normal use.
You may be able to have the battery replaced, but the cost (parts and labor) is likely to exceed the price of a brand new 4th gen shuffle (about $50).
If you are good a fixing small electronic devices, this web site has repair manuals
(It's not designed to be taken apart by the user.)